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A132845
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Triangle, read by rows, where row n equals row n of matrix power A132844^n for n>=0, where triangle A132844 is defined by: A132844(n,k) = T( [(n+k)/2], k) for n>=k>=0.
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5
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1, 1, 1, 3, 2, 1, 13, 9, 3, 1, 73, 42, 18, 4, 1, 466, 270, 95, 30, 5, 1, 3309, 1785, 693, 179, 45, 6, 1, 25425, 13657, 4893, 1463, 301, 63, 7, 1, 209717, 108606, 40506, 11104, 2726, 468, 84, 8, 1, 1837168, 943677, 338277, 99177, 22239, 4653, 687, 108, 9, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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FORMULA
| T(n,k) = [A132844^n](n,k) where A132844(n,k) = T( [(n+k)/2], k) for n>=k>=0.
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EXAMPLE
| Triangle T begins:
1;
1, 1;
3, 2, 1;
13, 9, 3, 1;
73, 42, 18, 4, 1;
466, 270, 95, 30, 5, 1;
3309, 1785, 693, 179, 45, 6, 1;
25425, 13657, 4893, 1463, 301, 63, 7, 1;
209717, 108606, 40506, 11104, 2726, 468, 84, 8, 1;
1837168, 943677, 338277, 99177, 22239, 4653, 687, 108, 9, 1;
16995545, 8534290, 3110310, 873440, 213415, 40707, 7440, 965, 135, 10, 1; ...
Triangle A132844 begins:
1;
1, 1;
1, 1, 1;
1, 2, 1, 1;
3, 2, 3, 1, 1;
3, 9, 3, 4, 1, 1;
13, 9, 18, 4, 5, 1, 1; ...
where column k of A132844 equals column k of T with terms repeated;
then row n of T equals row n of A132844^n as illustrated below.
Matrix square A132844^2 begins:
1;
2, 1;
3, 2, 1; <-- row 2 of T
5, 5, 2, 1;
12, 9, 7, 2, 1;
25, 31, 13, 9, 2, 1; ...
Matrix cube A132844^3 begins:
1;
3, 1;
6, 3, 1;
13, 9, 3, 1; <-- row 3 of T
33, 22, 12, 3, 1;
87, 75, 31, 15, 3, 1; ...
Matrix 4-th power A132844^4 begins:
1;
4, 1;
10, 4, 1;
26, 14, 4, 1;
73, 42, 18, 4, 1; <-- row 4 of T
220, 151, 58, 22, 4, 1; ...
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PROG
| (PARI) {T(n, k)=local(M=matrix(n+1, n+1, r, c, if(r>=c, if(r<=c+1, 1, T((r+c)\2-1, c-1))))); (M^n)[n+1, k+1]}
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CROSSREFS
| Cf. A132844 (triangle); columns: A132846, A132847, A132848, A132849.
Sequence in context: A156628 A104980 A134090 * A129652 A154921 A127126
Adjacent sequences: A132842 A132843 A132844 * A132846 A132847 A132848
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KEYWORD
| nonn,tabl
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Sep 17 2007
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